This invention relates to combination of values generated by one or more pseudo-random sources (PRS).
A pseudo-random value, or set of values, can be used, for example, for a applications in which the pseudo-random value can be regenerated, but the value cannot be predicted, or such prediction would be very difficult or time consuming. In some examples, the pseudo-random value depends on an input value, often referred to as a “challenge” value. In some examples, the pseudo-random values comprise bits that are generated by circuitry that implements a function depend on device-specific characteristics, for example, based on device-to-device fabrication variation among a set of devices that are fabricated in a common manner, for example, according to the same semiconductor masks and fabrication conditions. Some examples of such functions have been referred to as Physical Unclonable Functions (PUFs). Examples of the device-specific characteristics include time-delay along electrical signal paths (e.g., through logic gates and conductive traces), and voltage thresholds of active semiconductor devices. In a number of previous approaches, the device specific quantities are binary, for example, based on a comparison of pairs of underlying device-specific characteristics. For example, US Pat. Pub. 2003/0204743A1, titled “Authentication of Integrated Circuits,” describes an approach in which a device-specific bit is generated according to the relative delay along two delay paths. As another example, US Pat. Pub. 2007/0250938A1, titled “Signal Generator Based Device Security,” describes an approach in oscillation frequencies are compared to determine device-specific bits.
Statistical properties of the generated pseudo-random values can affect their suitability for certain applications. For instance, statistical bias of the values may affect the strength of authentication and/or cryptographic techniques that make use of the values. Measures of a set of values include the National Institute of Standards and Technology (NIST) Statistical Test Suite for Randomness, which includes tests that measure statistical bias.